SOLUTION: The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...
Algebra ->
Sequences-and-series
-> SOLUTION: The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...
Log On
Question 142025: The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)... Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...
---------------------
a(4) = ar^3 = 56
a(6) = ar^5 = (7/8)
-----------
Divide a(6) by a(4) to get:
r^2 = 1/64
r = 1/8
-----------
Substitute to find a(1):
a(1/8)^3 = 56
a = 56/(1/8)^3 = 28672
--------------
GP: 28672, 28672(1/8), 28672(1/8)^2 etc
-----------------
S(n) = a[1-(r^n)]/[1-r]
Since 0
S(n) = a/[1-r] = 28672/[1-(1/8)] = 32768
=========================
Cheers,
Stan H.
(